Introduction

Leonhard Euler, 15 April 1707 – 18 September 1783, was a Swiss mathematician who discovered many many interesting things, in maths, physics, and astronomy. Leonhard_Euler.jpg

Euler's Law for 3D Objects

I like to use "Euler's Law" (sometimes called "Euler's Formula") when studying 3D objects. This law states that in any polyhedron (a 3D object formed by 2D shapes), if

  • V is the number of vertices,
  • F is the number of faces,
  • E is the number of edges,

then

V + F = E +2
I have a simple worksheet called that each student can fill out about a different 3D object which asks them to calculate V + F - E. You can then discuss with the group that everyone (who did the worksheet correctly) got the answer 2. Of course this activity is best done after some previous work on 3D objects, including learning the vocabulary, and especially making 3D objects out of nets. See the Teaching 3D Space page for more information.

This activity introduces some solid algebra, which I think is excellent in the early grades. I have used this successfully in year one with a high maths group. Not everyone got the final calculation right. There is a reasonably simple explanation of the formula on mathsisfun.

Seven Bridges of Konigsberg

The town of Konigsberg, now called Kaliningrad, had seven bridges joining various parts of the town including two islands. Someone decided to wonder whether it would be possible to visit all the parts of the town crossing the bridges only once. Euler showed that this was impossible, and this led to a completely new area of mathematics called graph theory, which is very useful in computer networks, sociology and biology.

Euler's Disk

Euler's Disk is an educational toy where a spinning disk rolls and spins for a long time. You can see the same motion when you spin a coin on a flat surface. This seems to have been named after Euler because he derived some of the equations for the motion of the disk. The Wikipedia page on Euler's disk gives more information.

I have included it here because there are good YouTube videos of the disk, you could probably buy one for the classroom if you wanted (although they are a bit expensive), and you can do it with coins anyway, which is pretty easy.

More about Euler

There is a great Wikipedia article on Euler. Other interesting (from a primary maths perspective) points are

  • he became famous for solving the Seven Bridges of Konigsberg problem.
  • he worked with both Johann and Daniel Bernoulli, famous mathematicians from the interesting and famous Bernoulli family
  • he spent 14 years working at St Petersburg in Russia, before moving to Berlin, where he worked for 25 years, writing over 380 articles.
  • he started attending lectures at the local university at the age of 13.

Sources and Other References